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Breaking Symmetry of Interchangeable Variables and Values
"... A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, p ..."
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A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, pruning all symmetric values is NPhard. We introduce a new global constraint called SIGLEX and its GAC propagator for pruning some (but not necessarily all) symmetric values. We also investigate how different postings of the SIGLEX constraints affect the pruning performance during constraint solving. Finally, we test these static symmetry breaking constraints experimentally for the first time.
Transforming and refining abstract constraint specifications
 In Proceedings of the Sixth Symposium on Abstraction, Reformulation and Approximation, volume 3607 of Lecture Notes in Computer Science
, 2005
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Modelling Equidistant Frequency Permutation Arrays: An Application of Constraints to Mathematics
"... Abstract Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that an ..."
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Abstract Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that any pair of codewords are a given uniform Hamming distance apart. The equidistant case is of special interest given the result that any optimal constant composition code is equidistant. This paper presents, compares and combines a number of different constraint formulations of this problem class, including a new method of representing permutations with constraints. Using these constraint models, we are able to establish several new results, which are contributing directly to mathematical research in this area. 3 1
Removing propagation redundant constraints in redundant modeling
 ACM Transactions on Computational Logic
, 2007
"... A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically ..."
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Cited by 8 (3 self)
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A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically implied by others in the problem model. However, some redundant constraints are propagation redundant and hence do not contribute additional propagation information to the constraint solver. Redundant constraints arise naturally in the process of redundant modeling where two models of the same problem are connected and combined through channeling constraints. In this paper, we give general theorems for proving propagation redundancy of one constraint with respect to channeling constraints and constraints in the other model. We illustrate, on problems from CSPlib
Boolean Equipropagation for Concise and Efficient SAT Encodings of Combinatorial Problems
"... We present an approach to propagationbased SAT encoding of combinatorial problems, Boolean equipropagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied to simplify the CNF encoding of the ..."
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Cited by 7 (5 self)
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We present an approach to propagationbased SAT encoding of combinatorial problems, Boolean equipropagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied to simplify the CNF encoding of the constraints. A key factor is that considering only a small fragment of a constraint model at one time enables us to apply stronger, and even complete, reasoning to detect equivalent literals in that fragment. Once detected, equivalences apply to simplify the entire constraint model and facilitate further reasoning on other fragments. Equipropagation in combination with partial evaluation and constraint simplification provide the foundation for a powerful approach to SATbased finite domain constraint solving. We introduce a tool called BEE (BenGurion Equipropagation Encoder) based on these ideas and demonstrate for a variety of benchmarks that our approach leads to a considerable reduction in the size of CNF encodings and subsequent speedups in SAT solving times. 1.
Extensible Automated Constraint Modelling
"... In constraint solving, a critical bottleneck is the formulation of an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of const ..."
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Cited by 5 (4 self)
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In constraint solving, a critical bottleneck is the formulation of an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of constraint modelling by automatically producing constraint models from their specifications in the abstract constraint specification language ESSENCE. A set of rules is used to refine an abstract specification into a concrete constraint model. We demonstrate that this set of rules is readily extensible to increase the space of possible constraint models CONJURE can produce. Our empirical results confirm that CONJURE can reproduce successfully the kernels of the constraint models of 32 benchmark problems found in the literature.
GAPLex: Generalised Static Symmetry Breaking
"... We describe a novel algorithm that statically breaks symmetry in CSPs by using computational group theory during search. This algorithm extends and generalises the commonly used “double lex ” method for breaking symmetry in matrices. We show that our new symmetry breaking method, GAPLex, is sound (w ..."
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We describe a novel algorithm that statically breaks symmetry in CSPs by using computational group theory during search. This algorithm extends and generalises the commonly used “double lex ” method for breaking symmetry in matrices. We show that our new symmetry breaking method, GAPLex, is sound (will neither lose solutions nor return incorrect solutions) and complete (will return exactly one member from each class of symmetrically equivalent solutions). We demonstrate that our implementation of GAPLex is competitive with other methods, being effectively applicable to CSPs with large domains and less than full variable and/or value symmetry. We also describe how GAPLex can be combined with incomplete symmetry breaking methods – such as doublelex – to provide fast and complete symmetry breaking. We believe this to be the first method that successfully combines the posting of symmetry breaking constraints before search, with symmetry breaking by analysis of search states. 1
Symmetry Breaking by Nonstationary Optimisation
, 2008
"... We describe a new partial symmetry breaking method that can be used to break arbitrary variable/value symmetries in combination with depth first search, static value ordering and dynamic variable ordering. The main novelty of the method is a new dominance detection technique based on local search i ..."
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We describe a new partial symmetry breaking method that can be used to break arbitrary variable/value symmetries in combination with depth first search, static value ordering and dynamic variable ordering. The main novelty of the method is a new dominance detection technique based on local search in the symmetry group. It has very low time and memory requirements, yet in preliminary experiments on BIBD design it breaks most symmetries and is competitive with several other methods.
Necessary Conditions for Constraintbased Register Allocation and Instruction Scheduling
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Generating Effective Constraint Programs: An Application of Automated Reasoning
"... Constraint programming has proven to be successful at solving a wide range of problems including important industrial problems. To solve a problem, one first “models ” it by characterising its solutions by the constraints ..."
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Constraint programming has proven to be successful at solving a wide range of problems including important industrial problems. To solve a problem, one first “models ” it by characterising its solutions by the constraints